Abstract
Integrated information theory (IIT) was initially proposed to describe human consciousness in terms of intrinsic-causal brain network structures. Particularly, IIT 3.0 targets the system’s cause–effect structure from spatio-temporal grain and reveals the system’s irreducibility. In a previous study, we tried to apply IIT 3.0 to an actual collective behaviour in Plecoglossus altivelis. We found that IIT 3.0 exhibits qualitative discontinuity between three and four schools of fish in terms of value distributions. Other measures did not show similar characteristics. In this study, we followed up on our previous findings and introduced two new factors. First, we defined the global parameter settings to determine a different kind of group integrity. Second, we set several timescales (from to s). The results showed that we succeeded in classifying fish schools according to their group sizes and the degree of group integrity around the reaction time scale of the fish, despite the small group sizes. Compared with the short time scale, the interaction heterogeneity observed in the long time scale seems to diminish. Finally, we discuss one of the longstanding paradoxes in collective behaviour, known as the heap paradox, for which two tentative answers could be provided through our IIT 3.0 analysis.
Highlights
We mainly focused on the average Φ values (denoted as hΦ( N )i) for all collective states (2 N for N fish schools)
Before we get into the details of the analysis of the classification, we review the meaning of the relationship between the Φ value and the minimum-information partition (MIP) cut
The information theory (IIT) analysis for the collective behaviour forces us to shift our focus from an external perspective to an internal perspective
Summary
Global dynamic patterns in swarming [1,2,3,4,5,6], schooling (of fish) [7,8,9,10,11], flocking (of birds) [12,13,14,15,16,17], genes [18], proteins [19], or neural networks [20,21,22,23], emerge from local interactions between self-organising individuals or components Despite their complexity, these collective systems are capable of processing information efficiently in critical conditions; for example, individuals making a swift response [14,15,16] or a group making a good decision [24,25,26] in a changing environment.
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